Anomalous diffusion and lévy flights in a two-dimensional time periodic flow

Abstract

One of the main consequences of chaos is that transport is enhanced with respect to the fluid at rest, where only molecular diffusion is present. Considering long times and spatial scales much larger than the length scale of the velocity field, particles typically diffuse with a diffusion constant, usually much bigger than the molecular one. Nevertheless there are some important physical systems in which the particle motion is not a normal diffusive process: in such a case one speaks of anomalous diffusion. In this paper, anomalous diffusion is experimentally studied in an oscillating two-dimensional vortex system. In particular, scalar enhanced diffusion due to the synchronization between different characteristic frequencies of the investigated flow (i.e., resonance) is investigated. The flow has been generated by applying an electromagnetic forcing on a thin layer of an electrolyte solution and measurements are made through image analysis. In particular, by using the Feature Tracking (FT) technique, we are able to obtain a large amount of Lagrangian data (i.e., the seeding density can be very high and trajectories can be followed for large time intervals) and transport can be characterized by analyzing the growth of the variance of particle displacements versus time and the dependence of the diffusion coefficient on the flow characteristic frequencies.